TSTP Solution File: GRP568-1 by SNARK---20120808r022
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP568-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:39:27 EDT 2022
% Result : Unsatisfiable 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of clauses : 36 ( 36 unt; 0 nHn; 4 RR)
% Number of literals : 36 ( 35 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(X,double_divide(double_divide(Y,double_divide(X,Z)),double_divide(identity,Z))),double_divide(identity,identity)) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(multiply,axiom,
multiply(X,Y) = double_divide(double_divide(Y,X),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(inverse,axiom,
inverse(X) = double_divide(X,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(identity,axiom,
identity = double_divide(X,inverse(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(prove_these_axioms_4,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_4) ).
cnf(6,plain,
multiply(X,Y) = inverse(double_divide(Y,X)),
inference('REWRITE',[status(thm)],[multiply,inverse,theory(equality)]) ).
cnf(7,plain,
inverse(double_divide(b,a)) != inverse(double_divide(a,b)),
inference('REWRITE',[status(thm)],[prove_these_axioms_4,6,theory(equality)]) ).
cnf(8,plain,
double_divide(double_divide(X,double_divide(double_divide(Y,double_divide(X,Z)),double_divide(identity,Z))),inverse(identity)) = Y,
inference('REWRITE',[status(thm)],[single_axiom,inverse,theory(equality)]) ).
cnf(9,plain,
double_divide(double_divide(X,double_divide(double_divide(Y,inverse(X)),inverse(identity))),inverse(identity)) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,inverse,theory(equality)]),inverse,theory(equality)]) ).
cnf(10,plain,
double_divide(double_divide(X,double_divide(inverse(Y),double_divide(identity,inverse(X)))),inverse(identity)) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,identity,theory(equality)]),inverse,theory(equality)]) ).
cnf(11,plain,
double_divide(double_divide(X,inverse(double_divide(Y,double_divide(X,inverse(identity))))),inverse(identity)) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,identity,theory(equality)]),inverse,theory(equality)]) ).
cnf(13,plain,
double_divide(inverse(X),inverse(identity)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9,identity,theory(equality)]),inverse,identity,theory(equality)]) ).
cnf(14,plain,
double_divide(double_divide(identity,double_divide(X,inverse(identity))),inverse(identity)) = double_divide(Y,double_divide(double_divide(X,inverse(Y)),inverse(identity))),
inference('PARAMODULATE',[status(thm)],[9,9,theory(equality)]) ).
cnf(15,plain,
double_divide(double_divide(identity,double_divide(X,inverse(identity))),inverse(identity)) = double_divide(Y,double_divide(double_divide(X,double_divide(Y,Z)),double_divide(identity,Z))),
inference('PARAMODULATE',[status(thm)],[9,8,theory(equality)]) ).
cnf(16,plain,
double_divide(double_divide(double_divide(identity,double_divide(X,inverse(identity))),inverse(identity)),inverse(identity)) = X,
inference('REWRITE',[status(thm)],[8,15,theory(equality)]) ).
cnf(18,plain,
double_divide(double_divide(identity,X),inverse(identity)) = double_divide(identity,double_divide(X,inverse(identity))),
inference('PARAMODULATE',[status(thm)],[9,16,theory(equality)]) ).
cnf(19,plain,
double_divide(double_divide(double_divide(identity,X),inverse(identity)),inverse(identity)) = double_divide(Y,double_divide(double_divide(X,inverse(Y)),inverse(identity))),
inference('REWRITE',[status(thm)],[14,18,theory(equality)]) ).
cnf(21,plain,
double_divide(double_divide(double_divide(identity,X),inverse(identity)),inverse(identity)) = double_divide(Y,double_divide(double_divide(X,double_divide(Y,Z)),double_divide(identity,Z))),
inference('REWRITE',[status(thm)],[15,18,theory(equality)]) ).
cnf(23,plain,
identity = inverse(identity),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[18,identity,theory(equality)]),13,inverse,theory(equality)]) ).
cnf(24,plain,
inverse(double_divide(X,double_divide(inverse(Y),double_divide(identity,inverse(X))))) = Y,
inference('REWRITE',[status(thm)],[10,inverse,23,theory(equality)]) ).
cnf(25,plain,
inverse(double_divide(X,inverse(double_divide(Y,inverse(X))))) = Y,
inference('REWRITE',[status(thm)],[11,inverse,23,theory(equality)]) ).
cnf(26,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[13,inverse,23,theory(equality)]) ).
cnf(27,plain,
inverse(double_divide(identity,X)) = double_divide(identity,inverse(X)),
inference('REWRITE',[status(thm)],[18,inverse,23,theory(equality)]) ).
cnf(28,plain,
inverse(double_divide(X,double_divide(inverse(Y),inverse(double_divide(identity,X))))) = Y,
inference('REWRITE',[status(thm)],[24,27,theory(equality)]) ).
cnf(29,plain,
double_divide(identity,X) = double_divide(Y,inverse(double_divide(X,inverse(Y)))),
inference('REWRITE',[status(thm)],[19,26,inverse,23,theory(equality)]) ).
cnf(30,plain,
inverse(double_divide(identity,X)) = X,
inference('REWRITE',[status(thm)],[25,29,theory(equality)]) ).
cnf(32,plain,
inverse(double_divide(X,double_divide(inverse(Y),X))) = Y,
inference('REWRITE',[status(thm)],[28,30,theory(equality)]) ).
cnf(33,plain,
inverse(X) = double_divide(Y,double_divide(double_divide(X,double_divide(Y,Z)),double_divide(identity,Z))),
inference('REWRITE',[status(thm)],[21,30,inverse,23,theory(equality)]) ).
cnf(36,plain,
inverse(X) = double_divide(identity,X),
inference('PARAMODULATE',[status(thm)],[26,30,theory(equality)]) ).
cnf(37,plain,
inverse(X) = double_divide(Y,double_divide(double_divide(X,double_divide(Y,Z)),inverse(Z))),
inference('REWRITE',[status(thm)],[33,36,theory(equality)]) ).
cnf(39,plain,
inverse(X) = double_divide(Y,double_divide(inverse(X),Y)),
inference('PARAMODULATE',[status(thm)],[26,32,theory(equality)]) ).
cnf(41,plain,
X = double_divide(Y,double_divide(X,Y)),
inference('PARAMODULATE',[status(thm)],[39,26,theory(equality)]) ).
cnf(42,plain,
X = double_divide(double_divide(Y,X),Y),
inference('PARAMODULATE',[status(thm)],[41,41,theory(equality)]) ).
cnf(46,plain,
X = double_divide(Y,double_divide(Y,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[37,42,theory(equality)]),26,theory(equality)]) ).
cnf(52,plain,
double_divide(X,Y) = double_divide(Y,X),
inference('PARAMODULATE',[status(thm)],[42,46,theory(equality)]) ).
cnf(54,plain,
$false,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[7,52,theory(equality)]),theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP568-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.11/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 21:06:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.45 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.46 *
% 0.20/0.46 *
% 0.20/0.47 #<PACKAGE "SNARK-USER">
% 0.20/0.47 *
% 0.20/0.47 SNARK-TPTP-OPTIONS
% 0.20/0.47 *
% 0.20/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.47 (USE-FACTORING :POS)
% 0.20/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.47 *
% 0.20/0.47 "."
% 0.20/0.47 *
% 0.20/0.47 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T21:06:29
% 0.20/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n013.cluster.edu at 2022-06-13T21:06:29
% 0.20/0.48
% 0.20/0.51 ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 0.20/0.51
% 0.20/0.51 #||
% 0.20/0.51 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.51 % SZS output start Refutation
% See solution above
% 0.20/0.52 ||#
% 0.20/0.52
% 0.20/0.52 ; Summary of computation:
% 0.20/0.52 ; 201 formulas have been input or derived (from 24 formulas).
% 0.20/0.52 ; 54 (27%) were retained. Of these,
% 0.20/0.52 ; 35 (65%) were simplified or subsumed later,
% 0.20/0.52 ; 19 (35%) are still being kept.
% 0.20/0.52 ;
% 0.20/0.52 ; Run time in seconds excluding printing time:
% 0.20/0.52 ; 0.001 2% Read assertion file (1 call)
% 0.20/0.52 ; 0.000 0% Assert (5 calls)
% 0.20/0.52 ; 0.008 18% Process new row (194 calls)
% 0.20/0.52 ; 0.000 0% Resolution (46 calls)
% 0.20/0.52 ; 0.002 4% Paramodulation (23 calls)
% 0.20/0.52 ; 0.002 4% Forward simplification (164 calls)
% 0.20/0.52 ; 0.006 13% Backward simplification (54 calls)
% 0.20/0.52 ; 0.003 7% Ordering (391 calls)
% 0.20/0.52 ; 0.000 0% Sortal reasoning (32 calls)
% 0.20/0.52 ; 0.000 0% Purity testing (1 call)
% 0.20/0.52 ; 0.023 51% Other
% 0.20/0.52 ; 0.045 Total
% 0.20/0.52 ; 0.049 Real time
% 0.20/0.52 ;
% 0.20/0.52 ; Term-hash-array has 153 terms in all.
% 0.20/0.52 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.20/0.52 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.20/0.52 ; Path-index has 57 entries (63 at peak, 196 added, 139 deleted).
% 0.20/0.52 ; Path-index has 305 nodes (320 at peak, 565 added, 260 deleted).
% 0.20/0.52 ; Trie-index has 57 entries (63 at peak, 196 added, 139 deleted).
% 0.20/0.52 ; Trie-index has 160 nodes (269 at peak, 819 added, 659 deleted).
% 0.20/0.52 ; Retrieved 328 generalization terms in 674 calls.
% 0.20/0.52 ; Retrieved 103 instance terms in 58 calls.
% 0.20/0.52 ; Retrieved 303 unifiable terms in 149 calls.
% 0.20/0.52 ;
% 0.20/0.52 ; The agenda of rows to process has 3 entries:
% 0.20/0.52 ; 3 with value 20
% 0.20/0.52 ; The agenda of rows to give has 6 entries:
% 0.20/0.52 ; 1 with value (4 17) 1 with value (4 22) 1 with value (4 23)
% 0.20/0.52 ; 3 with value (4 20)
% 0.20/0.52 Evaluation took:
% 0.20/0.52 0.05 seconds of real time
% 0.20/0.52 0.044707 seconds of user run time
% 0.20/0.52 0.005075 seconds of system run time
% 0.20/0.52 0 calls to %EVAL
% 0.20/0.52 0 page faults and
% 0.20/0.52 5,097,688 bytes consed.
% 0.20/0.52 :PROOF-FOUND
% 0.20/0.52 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T21:06:29
% 0.20/0.52 :PROOF-FOUND
% 0.20/0.52 *
%------------------------------------------------------------------------------